They really are the Odd Couple of economic policy. On one side of the Atlantic is Alan Greenspan, who last week stepped down as Chairman of the Federal Reserve after nearly two decades of mastering the financial universe. On the other is Gordon Brown, the Chancellor of the Exchequer, who last week was still Chancellor of the Exchequer after nearly one decade of wishing he was Prime Minister.

Mr Greenspan is revered today as only the Oracle of Delphi was revered in the ancient world. Yet before he went to the Fed, he was regarded as something of a Right-wing maverick. He was a disciple of Ayn Rand, whose theory of Objectivism might best be summed up as the veneration of unfettered capitalism. Mr Brown had a rather different mentor in his formative years. He wrote his PhD about that Red Clyde firebrand, James Maxton, who dedicated his life to the denigration of unfettered capitalism.

So there was something distinctly bizarre about the report last week that, Mr Greenspan is now to become an unpaid "honorary" adviser to HM Treasury. I'm not sure which is more bizarre; that Mr Brown should want advice from Mr Greenspan, or that Mr Greenspan should be willing to give it for free. (Or is that "honorary" as in: "We'd be honoured if he ever came into the office, but he never does"?)

What can have brought this odd couple together? The answer would seem to be Adam Smith. Last year, at Mr Brown's instigation, Mr Greenspan gave the annual Smith lecture in Kirkaldy, the great Scottish economist's birthplace. No Scotsman - even the most wild-eyed socialist - can resist it when a foreigner acknowledges that it was one of us who invented economic liberalism.

Naturally, I welcome Mr Brown's conversion to Smith's principle that the "invisible hand" of the market will always out-perform the deadening hand of the state when it comes to allocating resources in an economy. And I can quite see why it took an American to make him see the light. There's nothing like a few holidays at Martha's Vineyard to convince a man that Smith got it right in the Wealth of Nations. After all, a very large part of the wealth of nations seems to spend the summer there, too. And it wasn't the planned economy that made those folks rich.

Still, there remains a profound disconnect between Mr Brown's Smithian rhetoric and the sorry reality of his record as Chancellor. So we must hope that when Mr Greenspan arrives at Number 11 Downing Street for his first session as Mr Brown's honorary adviser, he will not - as has been his wont for the past 19 years - mince his words:

AG: "Gordon, I have to level with you. The British economy is in a mess. And it's your fault. You inherited an economy that had been saved from ruin by Margaret Thatcher. You did one thing right, which was to make the Bank of England independent. But to call the rest of your time as Chancellor a success would be - to coin a phrase - irrational exuberance.

"Nearly a third of the new jobs created in the UK since 1997 have been in the public sector. You've thrown billions at an inefficient, state-run heath service. Meanwhile, productivity in Britain lags behind not just the US but even Italy. And of all the economies in the Organisation for Economic Cooperation and Development, yours has the second-highest proportion of young people who are low-skilled. Smith taught that economies should play to their strengths - their comparative advantage. Well, those kids don't have any."

How might the Chancellor reply to this painful indictment? Perhaps like this:

GB: "Thanks, Alan old boy, but actually those aren't the things I wanted you to advise me about. There's another set of problems that are worrying me more.

"First, I'm a little nervous about the growth of public sector borrowing. Second, there's been one hell of a housing bubble here and I'm worried that as it deflates we're going to slide into recession. Worst of all, our pensions system seems to be heading for meltdown. And I nearly forgot our current account deficit, which just refuses to go away. I wonder if these problems sound familiar to you?"

AG: "Okay, Gordon, it's a fair cop. The truth is that I'm not quite as big a genius as everyone was saying last Tuesday. Sure I got the big things right. Inflation is lower and growth steadier than it was when I took over the Fed in 1987. I've got the American economy through not one but two stock market crashes, to say nothing of a direct terrorist hit on downtown Manhattan.

"But my real legacy to my successor is a conundrum. You see, monetary policy used to be pretty straightforward. In a recession, you cut short-term interest rates. When the economy over-heated, you put them back up. But I've spent the better part of the past two years putting up American interest rates and - I have to admit it - no one seems to have noticed.

"The dollar has weakened only a little and long-term rates haven't budged at all. So our housing bubble is still going strong. And American families aren't saving a cent. In fact they just keep borrowing more and more against their homes, and then heading off to the shopping malls to spend it. Meanwhile, as a percentage of gross domestic product, our current account deficit is more than twice the size of yours.

"I just don't get it. I've raised rates 14 times since June 2004, from 1 per cent to 4.5 per cent. If quadrupling the cost of borrowing can't cool things down in the US, I don't know what can. Is it just that the rate hikes are taking time to have an effect? Are long-term rates being artificially depressed by Asian central banks' purchases, a lack of activity on the corporate bond market and a rush by institutions to hold long-dated bonds? Or is everybody out there just dreaming that inflation is no longer something they need to worry about thanks to globalisation?

"One thing's for sure, I breathed a sigh of relief when I walked out of my office for the last time back on Tuesday. Come to think of it, I guess that's the way you'll feel when you finally get to move next door into Number 10.

"For, as you were implying, my dear Gordon, my conundrum is not peculiar to the United States. In Britain the situation may even be worse. I gather that changes to the regulations governing defined-benefit pension schemes are driving long-term rates even lower than short-term rates by effectively forcing institutions to buy all the gilt-edged securities they can get their hands on.

"That may sound a little technical to most voters, but when the effect is to drive down annuity rates close to zero, retirees start feeling some pretty un-technical pain. And if they figure out that it's all the fault of the Treasury, then I don't give much for your election chances against that smart young Mr Cameron.

"Speaking of which, I must be going. Much as I've enjoyed being your honorary adviser, it turns out that the Conservatives have just invited Greenspan Associates to give them some non-honorary advice on economic policy. Given that they're the party that actually believes in Adam Smith - and that they're actually going to pay me - I feel bound to accept.

"Well, so long, Gordon. I do hope you time your next career move as well as I've timed mine."